1. Field
The present invention generally relates to techniques for charging/discharging a rechargeable battery. More specifically, the present invention relates to a method and apparatus for estimating state of charge and the associated uncertainty based on measured relaxing voltage of the battery.
2. Related Art
Rechargeable lithium-ion batteries are presently used to provide power in a wide variety of systems, including smartphones, wireless devices, laptop computers, cordless power tools and electric vehicles. State of charge (SOC) is a measure of a present capacity of a battery expressed in percentage points (0%=empty; 100%=full). Accurately estimating the state of charge for a battery is fundamental to basic battery management, such as determining full charge capacity, reserve capacity, and battery health.
State of charge of a battery can be estimated using a number of techniques. For example, a voltage-based state-of-charge estimation technique first measures a resting voltage of the battery, and the state of charge can then be derived from the resting voltage value based on a predetermined voltage vs. SOC relationship which has been calibrated for the battery. This technique is straightforward but can be inaccurate if the battery is not fully rested when the voltage measurement is taken. Note that after current stops flowing to the cell, it can take a long time, often up to hours, for the cell to become fully rested. In contrast, a coulomb-counting-based state-of-charge estimation technique determines the state of charge for a battery by measuring the charge that flows in and out of the battery. However, this technique also has associated sources of uncertainty, which include, but are not limited to, measurement offset errors, and slow changes in the battery's coulomb capacity.
Another state-of-charge estimation technique combines the voltage-based technique with the coulomb-counting-based technique to achieve a higher accuracy. Note that when combining the coulomb-counting-based SOC estimate and the voltage-based SOC estimate, it is necessary to take into account uncertainties from both techniques. It is generally safe to overestimate these uncertainties since the uncertainty of combined state-of-charge estimates will encompass the true state of charge. However, if an uncertainty is underestimated or missing from consideration, more serious problems can occur. For example, the two SOC estimates can appear inconsistent with each other, thereby causing a safety condition to be triggered, while in reality the problem is simply that the uncertainty in one of the estimates is significantly underestimated.
As mentioned above, a significant source of uncertainty in the combined estimate not yet taken into account is caused by the error in the voltage-based SOC estimate due to a not fully rested cell. In principle, the open circuit voltage for a fully relaxed bank (of cells) is used with pre-characterized open circuit voltage (OCV) curves to estimate the voltage-based state-of-charge independent of the coulomb count. The problem arises as a result of how the “fully relaxed” state is defined. For example, in one voltage-based technique, a bank is considered fully relaxed when the magnitude of the derivative of the voltage is below a threshold of 4 μV/sec. In another voltage-based technique, a fully relaxed bank is defined as the magnitude of the derivative of the voltage-based state-of-charge less than 0.5%/hr.
However, both of the above-described voltage-based techniques suffer from the residual error in the state-of-charge estimate due to a bank which is not fully relaxed. This problem is particularly troublesome at cold temperatures because in such conditions the relaxation process is long, and on flat parts of the OCV curve where the threshold values are reached, small changes in voltage can cause large changes in the state of charge. FIG. 1 illustrates how using derivatives to define a fully rested cell can lead to large errors at cold temperatures and at flat parts of the OCV curves. Note that at 58.6% state of charge it takes about 159 minutes for the derivative of the voltage-based state-of-charge to reach 0.5%/hr. At this point the state of charge is still not fully rested with a 0.6% residual error. Using the other fully relaxed definition, the voltage reaches 4 μV/sec at about 103 minutes with a 1.0% residual error. If this uncertainty is not taken into account, the difference between the voltage-based state-of-charge and the coulomb-counter-based state-of-charge can be large enough to incorrectly trigger a problem diagnosis, provided that the coulomb-counter-based state-of-charge uncertainty is relatively small.
Hence, what is needed is a method and an apparatus for accurately estimating a state of charge and the associated uncertainty for a relaxed battery without the above-described problems.